Previous Fields

Contact Methods

AIM

killfolksingers

Website URL

http://

ICQ

0

Profile Information

Location

San Francisco, CA

Interests

All sorts of literature, movies that make me laugh, just about anything else that makes me laugh, music (some of most genres, but particularly indie rock), health & fitness, great food (especially a good burger), giraffes, sneakers, beautiful & intelligent women, the people I love, the people I may grow to love, and myself<br /><br />I almost forgot to mention Diet Coke, the nectar of the gods!

This semester, the SFSU Objectivist Club will be engaging in an OPAR study group, which is open to students and non-students alike.
The study group will be of special interest to those who are auditing or enrolled in SARPO, as we will be more-or-less moving through OPAR along with SARPO, since several club members are enrolled in OAC.
The study group will meet weekly on Thursdays, at 5:00 pm, in either Rosa Parks conference room D or E of the Cesar Chavez Student Center on the SFSU campus. The specific room will change from week to week, but they are right next door to each other, so we should be very easy to find.
For more information, or to find out what the discussion topic for the upcoming week is, e-mail [email protected]
-Dave Zornek
[email protected]

The Objectivist Club of Berkeley and the SFSU Objectivist Club are co-hosting Andrew Berstein will to speak on "Global capitalism: The solution to world oppression." The lecture will be held Wednesday, April 26th at 7:30pm in 22 Warrens, on the Berkeley Campus.
For more information, feel free to PM me or e-mail [email protected]

It's not that complex, and I did give support, way back at the beginning. You asked for references of what, in the Objectivist theory of concepts gave rise to it, which I also gave. To repeat what I said earlier (since you seem to have forgotten): it follows from the idea of a fundamental characteristic as the one which causes the greatest number of others--characteristic which does not exist cannot be said to cause anything about an existent. I gave two references to support this claim: Rand's explanation of essential characteristics and her discussion of concepts formed on the basis of a non-existent.
I don't reject concepts like "caffeine-free;" in fact, it was my intention to cite that as a legitimate concept-by-negative. What I reject is a concept of "caffeine-free soda." (In fact, as applied to the concepts in this thread, I do not reject the concept of "non-self-referring," but I do reject the concept of "non-self-referring concept.") Those kind of concepts are the rare exceptions. Yes, there are thousands of them, but in comparison to the many, many more thousands of positive concepts, they are relatively rare.
Before I bow out of this discussion (this will be my last post, as my purpose has been met), I will summarize my reasons for rejection of a concept formed on the basis of a non-existent characteristic:
1) The Conceptual Common Denominator. "The units of a concept were differentiated--by means of a distinguishing characteristic(s)--from other existents possessing a commensurable characteristic, a 'Conceptual Common Denominator.'" (ITOE, 41) Attempting to form a concept on the basis of a characteristic some existent does not possess, one is attempting to form a concept on the basis, not of a differentiation between existents possessing a commensurable characteristic, but on the basis of an incommensurability--something which exists and something which doesn't.
2) The rule of fundamentality. "Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others." (ITOE, 45) This means that the fundamental characteristic must has some causal efficacy in relation to all of the other characteristics differentiating an existent from the other things sharing its CCD. Aside from the fact that no CCD can exist on the basis a non-existent characteristic, a non-existent characteristic cannot be said to have any causal effect on any of the other characteristics, or anything at all for that matter.
3) Rand's Razor of Concepts. "Concepts are not to be multiplied beyond necessity..." (ITOE, 72) There is no necessity of forming a concept of an existent on the basis of a non-existent characteristic, since "absence" is a valid concept, from which we can abstract the absence of specific things, yielding concepts-of-absence that may be used to modify other concepts in propositions without the need of forming new, invalid concepts.

Rand formulated two razors, both of which she mentions in ITOE. The one Peikoff refers two is mentioned only in the appendix, and she refers to it as the"original 'Rand's Razor.'" (ITOE, 251) The other is a "razor of concepts." (ITOE, 72)
I suggest that, until you have read those passages, you refrain from saying that no support has been given.
Secondly, I never said that negatives cannot ever be used. I said that, except in rare cases, they cannot be the proper basis for forming a concept. Rand specifically points out a few of such concepts (such as "nothing" and "non-existence") as examples of "invalid concepts." She also gives an example of a valid concept "absence" which is valid only in reference to the concept "presence," and can only be defined or formed in reference to it--concepts like this are precisely the very rare cases that I was talking about. (The concept of "absence" can be looked at as the fundamental concept-by-negation, as the others are all concepts of a things absence, like "caffeine-free," "non-physical," or "innocent." That does not mean that it is proper to for the concepts of "caffeine-free soda," "non-physical entity," or "innocent man," though--it just means that we have such adjectives to modify proper concepts as a means of describing those phenomena where they occur.)
[EDIT: That parenthetical is to be taken as my own identification, not Ayn Rand's.]
I've given a lot of references to ITOE, and I'm not going to copy them all in here for your convenience. I do request, though, that you stop claiming I haven't given any support for these things or asking for the support, when I've pointed you straight to it. The truth isn't that my claims go unsupported; the truth is that you've either ignored or been unable to look up the support I've given.

Having a hierarchy does not mean that extending a theory must be based only on the more fundamental facts that have already been established. What it means is that the later knowledge cannot contradict the more fundamental facts. It's not my theory; it's Ayn Rand's, so if you have a problem with her idea (which, admittedly, does not follow directly from the axioms) that one should not form new concepts unless there is some cognitive need for them, talk to her.
If you want my opinion on why she formulated her Razor, I think it stems from her view of epistemology as a practical science--that's pure speculation on my part, though.
Well, the problem Kyle brought to the table was about whether or not Ayn Rand's theory of concepts was susceptible to Russel's paradox, so the entire theory--all of it--everything she said in ITOE and elswhere on the subject of concepts--is fundamental to this problem.
My purpose in this thread isn't really to prove whether Ayn Rand's later principles follow from the earlier ones, but to show that her theory of concepts, when taken in its entirety does not lead to a contradiction. I have no interest in (nor do I think I'm properly qualified--yet) attempting to do the former, which is basically what you're asking me to do.
It is rationalism to confine yourself to a deductive proof from any set of axioms, regardless of the nature of those axioms. Most rationalists, historically, did adopt their axioms without regard to experience, but that's a separate issue. There are a great many quasi-Objectivists who adopt certain ideas of Objectivism, with regard to experience, but then apply them rationalistically. Dr. Peikoff has a whole lecture course specifically on this phenomena. ("Understanding Objectivism"--it's very expensive; I don't expect you to buy it.)
If you weren't asking for a deductive proof, then I retract my earlier statemtent, but that is the impression that I got.
Well, yeah. Deductive reason works very well for the things it works for, but it isn't the only kind of reasoning, and there are some things that you just can't learn by deduction.
Ayn Rand discusses this in chapter seven of ITOE, "The Cognitive Role of Concepts," the very same chapter where she introduces her aforementioned "razor." I'll warn you though, that she does not show it by a deductive method. Rather, she introspects and tells her observations.
The first thing I want to say is that I don't think I ever said "cognitive value" (I didn't go back and check, so if I did say that, I'll say right now that it was a mistake). What I said was "cognitive significance," which is different from a value judgment.
Secondly, the one point you bring up that does as have real cognitive significance is that forming this concept leads to a contradiction, which is precisely what makes a rejection of the concept warranted, as opposed to your claim that it is arbitrary.
Quite frankly, I'm astonished that you could possibly describe my claim that this concept is invalid (according to Objectivism) as arbitrary, considering the support I have drawn directly from Objectivist literature in favor of my position. At most, what you can claim is that the principles I've referenced are arbitrary, and you're certainly entitled to do that.
I'm not going to attempt to prove that these particular parts of Objectivism are correct. It isn't my purpose in this thread, and I don't fully grasp the validation of them myself--if I were an expert I wouldn't need to be enrolled in OAC, working to become one. What I do fully grasp, however, is that the points I've raise are a part of Objectivism, they are a part of Ayn Rand's theory, and that they cannot be ignored in an attempt to prove that her theory leads to a contradiction.

That depends on the context--what the units of the concept are, their place in the conceptual hierarchy, all sorts of thing. In the context of the particular concept(s) being discussed here, since there is a valid categorization being drawn, in order to validate the concepts, it needs to be shown that the differentiation leads to real consquences in the concepts themselves. So far, all that has been shown is a difference between sets which have been constructed from the concepts.
Yes, one does have to show that they ARE necessary, when called to task to do so. That is the principle of the onus of proof. Broadly, that means showing cognitive significance--that's too broad for you, though. If you're looking for something more concrete, it varies from concept to concept, and it is up to the person claiming cognitive significance to identify the concretes involved. Ayn Rand gives some specific examples in ITOE starting on page 72.
Not necessarily, it depends on how that aligns with our own knowledge of the particular units involved.
Objectivism says a great deal on concepts besides just how they are formed--a great deal. You can't say, prove it from the theory up to this point, but don't bring in anything else from that theory. This discussion is about more than just concept-formation, but the entire Objectivist approach to epistemology, which involves the entire theory of concepts presented in ITOE (aside from just the material on formation), in addition to a number of other articles scattered throughout the Objectivist literature. Objectivist epistemology does not end at concept-formation, nor does it even end at ITOE.
Moreover, it seems like your asking for a deduction from the axioms, which is (as many, many Objectivist intellectuals, including Ayn Rand, have pointed out) a method that is completely incompatible with Rand's theory. It is rationalism.
What is the reason? What does forming the new concepts offer to cognition that the a concept of "concept" and two other concepts of "self-inclusive" and "non-self-inclusive" don't?

The current referents of the concept are those of the past and the future. This is a crucial point in Objectivist epistemology. Concepts don't (at present) integrate that which exists right now, and then a year from now, integrate the things which exist then--they are atemporal. The measurement that the specific referents have to exist at some time is retained in the concept, but the specific time is completely omitted. I know of no concept which is an exception to this rule. Once you start talking in terms of the referents which exist right now, instead of all the referent of any era, you are no longer using a concept, but a frozen abstraction.
You might be able to make two categories of concepts: Concepts which, when listed in the form of a set, are fully-listable, and others which are not, but that doesn't mean you have grounds to form a concept. Here is where your nominalism comes into play. You are taking just any old differentiation and trying to make a concept out of it--which is adamantly not the way Objectivism approches concepts.
Ayn Rand put her own spin on Occam's Razor. Rand's Razor is: "concepts are not to be multiplied beyond necessity--the corrollary of which is: nor are they to be integrated in disregard of necessity." (ITOE, 72). You are guilty of the first. There is absolutely no significant cognitive or metaphysical reason to form the concept of "fully-listable concept." Every significant difference you have identified belongs to the sets themselves, so the difference is less fundamental than the concepts themselves. (And they are epistemological differences--there is absolutely no metaphysical difference between sets and concepts, since sets are a particular kind of concept.)
That's where he starts. Binswanger talks about that, forms the concept of number, and the rest goes from there.
It's more than just unfamiliar to Objectivists; in the way it's being done here, it's completely rejected by Objectivists. It's an attempt to deduce the properties of concretes from the abstractions, which is the opposite of the Objectivist theory of concepts. In Objectivism, we observe the properties of concretes, and abstract generalizations from them. (Not to say deduction is invalid--it certainly isn't--but it isn't a means of concept-formation.)

I would honestly love to be able to simplify it in a manner that's conducive to a message board, but I'm afraid I just wouldn't even know where to begin. He spends about an hour on the justification in the lecture, so I don't know that I could honestly and convincingly present the whole thing in a few paragraphs. He doesn't spend that long on irrational numbers specifically, but the justification, which invalidates a number of mathematical concepts as they are traditionally defined. Others that he discusses are negative numbers and fractions, as well as geometric concepts such as line, point, and plane, especially line.
Because of the fervor you've shown for mathematics in the past, I would really recommend it to you. Even on the points where I disagree with him (and there are a couple in the section on Physics), his analysis is really very enjoyable.

The big deal with the characteristic of "fully listable" is that it has nothing to do with the concepts themselves. It is a characteristic of sets you have constructed from the concepts. Since the concepts are more fundamental than the sets you constructed from them, characteristics of the sets cannot be fundamental, distinguishing characteristics which form the basis for forming the derivative concepts of NSRC vs. SRC.

In the case of methods, facility is the cause--it is the reason we create methods in the first place. The characteristic is only non-essential when you reject the idea of irrational number as a method rather than a number.
In any event, it's not really fruitful to quibble over the formation and definition of individual concepts--at least it's not something I'm particularly interested in doing.
Well, I told you where you could find such justification. In case you missed it, here's a link.

Concepts do have attributes, and they are existents, but concepts are not the ultimate referents of any concept save one. In all other cases, they are ultimate reducible to concretes. The difference between the concept of "concept" and the others is that it is an integration of concepts qua concretes, rather than concepts qua integrations of other concretes.

In Objectivism, an essential characteristic is the causal characteristic, not the result. Disagree with it all you like, but that isn't what Ayn Rand meant when she used the term. However most people define non-alcholic beer, it would not be considered a proper, philosophic definition under Objectivism.
No, it possesses the characteristic of being able to facilitate calculations that rational numbers cannot.
So what if it's far-flung. Lots of the ideas that arose from Objectivism are; far-flung-ness has no significance whatsoever.
I'll address anything else later. I'm away for the rest of the day probably.

Well, numbers are concepts of quantity, of a particular identification, i.e. action, of consciousness, so the causal existents involved are both the consciousness performing the identification and all of the actual instances of the quantities in reality. Mostly, though, in mathematics, we deal with concepts of method, so the causal entity involved is usually consciousness.
If you're asking for the positive characteristics:
An even number is a natural number which, when halved (by a consciousness) yields another natural number.
A prime is a number with exactly two natural divisors.